﻿ 船舶机械设备连接结构的损耗分析
 舰船科学技术  2023, Vol. 45 Issue (23): 162-165    DOI: 10.3404/j.issn.1672-7649.2023.23.029 PDF

Research on the loss of connection structures of ship mechanical equipment
WU Yan-fang
Chongqing Three Gorges University, School of Mechanical Engineering, Chongqing 404020, China
Abstract: This article analyzes the damping of the joint surface of ship connecting structures, focuses on studying the mathematical model of damping energy consumption, and provides a measurement method for damping; Analyze the vibration suppression performance of the ship's connecting structure, provide the impedance value of the straight spring oscillator with frequency variation curve and the vibration response with frequency variation curve, and explore the local constraint excitation end response and non excitation end response; Finally, the loss factor of the ship's connecting structure was analyzed.
Key words: ships     mechanical equipment     structural loss
0 引　言

1 船舶连接结构结合面阻尼分析 1.1 阻尼耗能的数学模型

 $F = {F_0}\sin \omega t = {F_0}{e^{j\omega t}}\text{，}$ (1)
 $\Delta = {\Delta _0}\sin \left( {\omega t - \alpha } \right) = {\Delta _0}{e^{j\left( {\omega t - \alpha } \right)}}\text{。}$ (2)

 ${k^*} = \frac{F}{\Delta } = \frac{{{F_0}}}{{{\Delta _0}}}{e^{i\alpha }} = k{e^{j\alpha }}\text{，}$ (3)

 $\delta W = \int {F{\mathrm{d}}\Delta = \text{π} {F_0}{\Delta _0}\sin \alpha } \text{，}$ (4)

 $W = \frac{1}{2}{F_0}\left( {{\Delta _0}\cos \alpha } \right)\text{。}$ (5)

 $\Delta W = \frac{{\delta W}}{{\alpha \pi }} = \frac{1}{2}{F_0}{\Delta _0}\sin \alpha \text{。}$ (6)

 $\eta = \frac{{\Delta W}}{W} = \tan \alpha \text{。}$ (7)

 $K' = K\left( {\cos \alpha + j\sin \alpha } \right)\text{，}$ (8)

 $\eta ' = \frac{{{Im} \left[ {{K^*}} \right]}}{{{Re} \left[ {{K^*}} \right]}}\text{。}$ (9)

1.2 阻尼的测量方法

 ${\boldsymbol{M}}\dot x + {\boldsymbol{C}}\dot x + {\boldsymbol{K}}x = f\left( x \right)\text{。}$ (10)

 ${\boldsymbol{M}}\dot x + \left( {{\boldsymbol{K}} + jG} \right)x = F{e^{j\omega t}}\text{。}$ (11)

 ${s^2} + 2\xi {\omega _n}s + \omega _n^2 = 0\text{，}$ (12)
 ${s_{1,2}} = \left( { - \xi \pm \sqrt {{\xi ^2} - 1} } \right){\omega _n}\text{。}$ (13)

 ${\omega _d} = {\omega _n}\sqrt {1 - {\xi ^2}} \text{，}$ (14)

 $\delta = \xi {\omega _n}T\text{，}$ (15)

 $\alpha = \frac{1}{{\sqrt {{{\left( {1 - \lambda } \right)}^2} + {{\left( {2\xi \lambda } \right)}^2}} }}\text{。}$ (16)

 ${\eta _q} = \frac{1}{{{{\left| Q \right|}_{\max }}}}\text{。}$ (17)
2 船舶连接结构抑振性能分析

 ${F_r} = {\omega ^2}{m_r}{\bar w_r}\text{，}$ (18)

 ${F'_r} = {k_r}\left( {{{\bar w}_r} - {w_r}\left( {{x_r},{y_r}} \right)} \right)\text{。}$ (19)

 ${k_r} = {\bar k_r}\left( {1 + j\eta } \right)\text{。}$ (20)

 ${Z_{Fr}} = \frac{{{\omega ^2}{m_r}{k_r}}}{{{k_r} - {\omega ^2}{m_r}}}\text{。}$ (21)

 图 1 直簧振子阻抗值随频率的变化 Fig. 1 The impedance value of a straight spring oscillator changes with frequency

 图 2 不同频率下振动响应变化情况 Fig. 2 Changes in vibration response at different frequencies

 图 3 局部约束激励端响应 Fig. 3 Local constraint excitation end response

 图 4 局部约束非激励端响应 Fig. 4 Local constraint non excitation end response
 $\omega = \sqrt {{Re} \left( {{\varOmega ^2}} \right)} \text{。}$ (22)
3 船舶连接结构的损耗因子分析

 $\left\{ {\begin{array}{*{20}{c}} {{p_1} = \omega {\eta _1}{E_1} + \omega {{\eta '}_{12}}{E_1} - \omega {{\eta '}_{12}}{E_2}} ，\\ {{p_2} = \omega {\eta _2}{E_2} + \omega {{\eta '}_{21}}{E_2} - \omega {{\eta '}_{21}}{E_1}} 。\end{array}} \right.$ (23)

 $\left\{ {\begin{array}{*{20}{c}} {{\eta _{s1}} = {\eta _1} + {{\eta '}_{12}} - {{\eta '}_{21}}E_{21}^{\left( 1 \right)}}，\\ {0 = {\eta _2} + {{\eta '}_{21}} - {{\eta '}_{12}}E_{12}^{\left( 1 \right)}} 。\end{array}} \right.$ (24)

 $\left\{ {\begin{array}{*{20}{c}} {{{\eta '}_{21}} = \dfrac{{E_{12}^{\left( 2 \right)}}}{{1 - E_{12}^{\left( 2 \right)}E_{21}^{\left( 1 \right)}}}{\eta _{s1}}} ，\\ {{{\eta '}_{12}} = \dfrac{{E_{21}^{\left( 1 \right)}}}{{1 - E_{12}^{\left( 2 \right)}E_{21}^{\left( 1 \right)}}}{\eta _{s2}}} 。\end{array}} \right.$ (25)

 ${\eta _{si}} = {\eta _i} + \sum\limits_{j = 1,j \ne i}^N {{\eta _{ij}}} \text{，}$ (26)

 ${E_i} = \frac{1}{2}M{\bar v^2} = \frac{1}{2}M{\omega ^2}{\bar \mu ^2}\text{。}$ (27)

 $\frac{{{E_2}}}{{{E_1}}} = \frac{{\displaystyle\sum\limits_{i = 1}^n {{m_{2i}}{{\left| {{v_{2i}}} \right|}^2}} }}{{\displaystyle\sum\limits_{j = 1}^n {{m_{1j}}{{\left| {{v_{1j}}} \right|}^2}} }}\text{。}$ (28)

 图 5 振子1受激励的响应 Fig. 5 Response of oscillator 1 under excitation

 图 6 振子2受激的响应 Fig. 6 Response of oscillator2 under excitation

 图 7 等效内损因子变化曲线 Fig. 7 Equivalent internal loss factor change curve
4 结　语

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